On Total Vertex-Edge Domination

Şahin, Bünyamin; Şahi̇n, Abdulgani̇

doi:10.20944/preprints201807.0195.v1

Cited by 5 publications

(9 citation statements)

References 5 publications

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“…They also gave the relationship between and , , for trees and graphs, and also gave formulas to determine the double ev-domination number of paths and cycles. Sahin and Sahin [13] proved that the total ev-dominating set problem is NP-hard for bipartite graphs. They also showed that ( − + 2 − 1)∕2 is the upper bound for for a tree  with order , leaves and supporting vertices.…”

Section: Related Workmentioning

confidence: 99%

Edge-Vertex Dominating Set in Unit Disk Graphs

Singireddy¹,

Basappa²

2021

Preprint

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Given an undirected graph = ( , ), a vertex ∈ is edge-vertex (ev) dominated by an edge ∈ if is either incident to or incident to an adjacent edge of . A set ⊆ is an edgevertex dominating set (referred to as ev-dominating set) of if every vertex of is ev-dominated by at least one edge of . The minimum cardinality of an ev-dominating set is the ev-domination number. The edge-vertex dominating set problem is to find a minimum ev-domination number. In this paper we prove that the ev-dominating set problem is NP-hard on unit disk graphs. We also prove that this problem admits a polynomial-time approximation scheme on unit disk graphs. Finally, we give a simple 5-factor linear-time approximation algorithm.

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Section: Related Workmentioning

confidence: 99%

Edge-Vertex Dominating Set in Unit Disk Graphs

Singireddy¹,

Basappa²

2021

Preprint

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“…Graph theory was firstly proposed by Euler in 1736 [4]. Recently, the theory has been successfully applied to areas in different disciplines [9,10,11]. Since the theory is based on relational combinations, it has essential role in representing combinatorial objects and mathematical combinations.…”

Section: Introductionmentioning

confidence: 99%

Some properties of the topological spaces generated from the simple undirected graphs

Sarı¹

2022

Sigma J Eng Nat Sci - Sigma Müh Fen Bil Derg

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Graph theory, which is used effectively in many fields from science to liberal arts, has very important place in our lives. As a result of this, the topological structure of the graphs is studied by many researchers. In this paper, we investigate the topological spaces generated by the graphs. The states of being an accumulation point and an interior point of a point in these spaces are examined. It is defined that relative topology on a subgraph of a graph. It is shown that this topology is different from the topology generated by this subgraph. Moreover, using the minimal adjacencies of vertices set of a graph, necessary and sufficient conditions for being 𝑇 ! -space, 𝑇 " -space and Hausdorff space of the topological space generated from this graph are presented. This enables to examine whether the topological space is 𝑇 ! , 𝑇 " and Hausdorff without obtaining the topology generated from the graph.

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“…e symbol c t ve (G) indicates the total ve-domination number of a graph G and c t ve (G) is equal to the minimum cardinality of a TVEDS. e total edge-vertex domination was presented in [14]. A subset B ⊆ E is a total edge-vertex dominating set (simply, TEVDS) of G, provided that B is an EVDS and every edge in B shares an endpoint with another edge in B. e symbol c t ev (G) indicates the total ev-domination number of a graph G and c t ev (G) is equal to the minimum cardinality of a TEVDS.…”

Section: Introductionmentioning

confidence: 99%

Further Results on Total Edge‐Vertex Domination

Şahi̇n

2022

Journal of Mathematics

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Total edge-vertex domination is a new total domination-type parameter. In this paper, the author shows that determining the total edge-vertex domination number in bipartite planar graphs is NP-complete. Also, the author obtains a structural relation between total domination number and total edge-vertex domination number and characterizes the trees whose total edge-vertex domination number is equal to total domination number.

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On Total Vertex-Edge Domination

Cited by 5 publications

References 5 publications

Edge-Vertex Dominating Set in Unit Disk Graphs

Edge-Vertex Dominating Set in Unit Disk Graphs

Some properties of the topological spaces generated from the simple undirected graphs

Further Results on Total Edge‐Vertex Domination

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